Multiple choice

From the top of a building of height k, the angle of depression of a car on the ground is x. What is the distance of the car from the foot of the building?

  1. k tan x

  2. k sin x

  3. k cot x

  4. k cos x
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The angle of depression x from the top of a building of height k to a car on the ground is equal to the angle of elevation from the car to the top. Thus, tan(x) = k / distance. Distance = k / tan(x) = k * cot(x).

AI explanation

The angle of depression from the building to the car equals the angle of elevation from the car to the top of the building. In the resulting right-angled triangle, the tangent of the angle x equals the height of the building divided by the distance of the car from the foot. Using the identity tan x equals 1 divided by cot x, we can rearrange the formula to find that the distance equals k multiplied by cot x.

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